Riesz representation theorem
The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes an important connection between a Hilbert space and its continuous dual space.
Connections1
Duality between vectors and continuous linear functionals
This theorem establishes that every continuous linear functional on a Hilbert space can be uniquely represented as an inner product with a fixed vector.